Combustion generated heat addition to a ducted supersonic stream—I. Theory

Abstract

A condition critical to the occurrence of ignition in a ducted supersonic stream has been proposed. By utilising this concept as a further boundary condition, a new approach to the solution of the aerothermodynamic equations relevant to combustion in a supersonic air stream flowing in a non-constant area duct has been made. This approach involves the duct characteristic with which to describe the combustion process. Although it must be emphasised that this approach leads only to an engineering solution, the duct law, T o T oi = ( A A i ) R TO has been found to satisfy the system of equations and can be considered to be the additional equation required to close the problem. The above temperature-area relationship, which established the critical Mach number at which thermal choking occurs as unity, can be used as an alternative to the Crocco pressure-area relationship which predicts a non-unity critical Mach number.